What Splinterz was proposing was something entirely different that doesn't take any consideration for where the dwarve's are in relation to each other, which I didn't agree with.
If you have a better solution, please, let us know.
I'm afraid the simplest solution might make the most sense here. I.e. scale everything to a range 0 to 1 (or 0% to 100%), linearly combine the aspects with the weights, and again renormalise to 0 to 1
Yeah, I think that's what I was going for with the skewed distribution (since you pointed out z-scores don't work for non normal data). now most of the data does follow a normalish scheme, but we could convert to % more accurately if we did a skewed distribution.
Well, my impression was that the problem isn't really that you don't fit the distributions properly (even though that is most likely true, too), but that it might not be ideal to combine the aspect values in the way you do. You say you don't like not taking into account how the dwarves compare to each other, but you'd still do that, only
after you computed their respective role scores.
It might help clarifying what kind of behaviour you want the measure to have. Intuitively, to decide whether someone would make a good fighter by looking at their strength, agility, sword skill etc., would you really want to do go "oh look, he's in the top 0.00001% of sword fighters in my population, he most be optimally suited to be a fighter! I don't even care that he's below average in strength and agility by a good amount!"?... even if essentially everyone is shitty at sword fighting in your fort, he just happens to be the least shitty by a tiny little bit?
Because as far as I understand, that's what the current calculation will be doing (in a situation where sword skill has a very low standard deviation -- doesn't even have to have a mean at zero! -- and he's a tiny bit above mean, and where he's below average in strength and agility but those happen to have large standard deviations). And as far as I can see, that is not necessarily going to go away with better fitting distributions -- he might still be in the top 0.000001% in terms of sword fighting (because depending on how you measure it, he
is.)
Sorry I didn't want to discourage you however! Maybe it's just a good idea to play around a bit with the different options. If you really need some more skewed distributions to fit your data, you might want to look into so-called
heavy-tailed distributions, such as the
log-normal distribution.